The maximum power exchange section is playing an important role in analyzing the interoperation of network microgrids. Mathematically, the problem is formulated into a weighted Max-Cut problem, which is non-deterministic polynomial-time hard (NP-hard). A Quantum Approximate Optimization Algorithm (QAOA) is introduced in this paper to search the approximate maximum power exchange sections in networked microgrids. QAOA is a hybrid quantum-classical algorithm, which uses a classical optimizer to train a parametrized quantum circuit. Layer number and angle parameters of the quantum circuit are discussed, which highly impact the performance of QAOA. Numerical examples on a typical reconfigurable networked microgrid system test and verify the effectiveness of QAOA in getting the maximum power exchange sections. This quantum computing implementation sheds light on the development of quantum algorithms to resolve the challenges in power systems that are hard to solve by classical computers.
The maximum power exchange section is playing an important role in analyzing the interoperation of network microgrids. Mathematically, the problem is formulated into a weighted Max-Cut problem, which is non-deterministic polynomial-time hard (NP-hard). A Quantum Approximate Optimization Algorithm (QAOA) is introduced in this paper to search the approximate maximum power exchange sections in networked microgrids. QAOA is a hybrid quantum-classical algorithm, which uses a classical optimizer to train a parametrized quantum circuit. Layer number and angle parameters of the quantum circuit are discussed, which highly impact the performance of QAOA. Numerical examples on a typical reconfigurable networked microgrid system test and verify the effectiveness of QAOA in getting the maximum power exchange sections. This quantum computing implementation sheds light on the development of quantum algorithms to resolve the challenges in power systems that are hard to solve by classical computers.
The Quantum Approximate Optimization Algorithm (QAOA) is applied to Networked Microgrids (NMs) in this paper to search for the maximum power exchange section, which is playing an essential role in operating NMs. Mathematically, obtaining the maximum power section is to solve a Max-Cut problem over the modeling graph of NMs. Considering the integration and fluctuations of Distributed Energy Resources (DERs), the maximum power section will change frequently. To efficiently get the section, QAOA provides a powerful solution by leveraging quantum resources. The performance of QAOA highly depends on the critical parameters of quantum circuits. We find the designed parameters for QAOA are still effective under wide range change of output power of energy resources. Tests on a typical NMs system verify the effectiveness of the QAOA method in efficiently searching for the maximum power sections of NMs.
The Quantum Approximate Optimization Algorithm (QAOA) is a promising approach for programming a near-term gate-based hybrid quantum computer to find good approximate solutions of hard combinatorial problems. However, little is currently know about the capabilities of QAOA, or of the difficulty of the requisite parameters optimization. Here, we study the performance of QAOA on the MaxCut combinatorial optimization problem, optimizing the quantum circuits on a classical computer using automatic differentiation and stochastic gradient descent, using QuantumFlow, a quantum circuit simulator implemented with TensorFlow. We find that we can amortize the training cost by optimizing on batches of problems instances; that QAOA can exceed the performance of the classical polynomial time Goemans-Williamson algorithm with modest circuit depth, and that performance with fixed circuit depth is insensitive to problem size. Moreover, MaxCut QAOA can be efficiently implemented on a gate-based quantum computer with limited qubit connectivity, using a qubit swap network. These observations support the prospects that QAOA will be an effective method for solving interesting problems on near-term quantum computers.
This paper reviews a hybrid quantum-classical distributed algorithm for NP-hard combinatorial optimization problems, which is embedded in IBM Qiskit's Alternating Direction Method of Multipliers (ADMM) optimizer. We demonstrate a proof of concept for solving Mixed-Integer Convex Programs (MICP) in power system applications using a use case on power distribution network reconfiguration in IBM quantum computers. Using the Qiskit ADMM optimizer, the MICP is decomposed into two subproblems: a quadratic unconstrained binary optimization (QUBO) solved by quantum algorithms and a convex one solved by classical solvers. Our essential contribution is integrating the Quantum Random Access Optimization (QRAO) into the quantum-classical distributed framework and the existing Quantum Approximate Optimization Algorithm (QAOA) implemented in the Qiskit ADMM Optimizer. QRAO utilizes Quantum Random Access Codes (QRACs) to minimize qubit requirements and utilizes quantum state rounding for solution extraction. We examine the impact of noise on solutions derived from QRAO and compare them with results from QAOA using a use case on network reconfiguration in response to faults in the power distribution system.
The max-cut problem (MCP) is a classic problem in the field of combinatorial optimization and has important applications in various fields, including statistical physics and image processing. However, except for some special cases, the MCP still encounters a non-deterministic polynomial complete problem (an NP-complete problem), and there is currently no known efficient classical algorithm that can solve it in polynomial time. The quantum approximate optimization algorithm (QAOA), as a pivotal algorithm in the noisy intermediate-scale quantum (NISQ) computing era, has shown significant potential for solving the MCP. However, due to the lack of quantum error correction, the reliability of computations in NISQ systems sharply declines as the circuit depth of the algorithm increases. Therefore, designing an efficient, shallow-depth, and low-complexity QAOA for the MCP is a critical challenge in demonstrating the advantages of quantum computing in the NISQ era.In this paper, according to the standard QAOA algorithm, we introduce Pauli Y rotation gates into the target Hamiltonian circuit for the MCP. By enhancing the flexibility of quantum trial functions and improving the efficiency of Hilbert space exploration within a single iteration, we significantly improve the performance of QAOA on the MCP.We conduct extensive numerical simulations using the MindSpore quantum platform, and compare the proposed RY-layer-assisted QAOA with standard QAOA and its existing variants, including MA-QAOA and QAOA+. The experiments are performed on various graph types, including complete graphs, 3-regular graphs, 4-regular graphs, and random graphs with edge probabilities between 0.3 and 0.5. Our results show that the RY-layer-assisted QAOA achieves higher approximation ratios in all graph types, particularly in regular and random graphs, where traditional QAOA variants are difficult to implement. Moreover, the proposed method exhibits strong robustness as the graph size increases, and can maintain high performance even for larger graphs. Importantly, the RY-layer-assisted QAOA requires fewer CNOT gates and has a lower circuit depth than the standard QAOA and its variants, making it more suitable for NISQ devices with limited coherence times and high error rates.In conclusion, the RY-layer-assisted QAOA provides a promising approach for solving MCP in the NISQ era. By improving the approximation ratio while reducing circuit complexity, this method demonstrates significant potential for practical quantum computing applications, thus paving the way for developing more efficient and reliable quantum optimization algorithms.
Abstract Quantum technology provides a ground-breaking methodology to tackle challenging computational issues in power systems, especially for Distributed Energy Resources (DERs) dominant cyber-physical systems that have been widely developed to promote energy sustainability. The systems’ maximum power or data sections are essential for monitoring, operation, and control, while high computational effort is required. Quantum Approximate Optimization Algorithm (QAOA) provides a promising means to search for these sections by leveraging quantum resources. However, its performance highly relies on the critical parameters, especially for weighted graphs. We present a data-driven QAOA, which transfers quasi-optimal parameters between weighted graphs based on the normalized graph density, and verify the strategy with 39, 774 instances. Without parameter optimization, our data-driven QAOA is comparable with the Goemans-Williamson algorithm. This work advances QAOA and pilots the practical application of quantum technique to power systems in noisy intermediate-scale quantum devices, heralding its next-generation computation in the quantum era.
This paper proposes an application algorithm based on a quantum approximate optimization algorithm (QAOA) for wireless scheduling problems. QAOA is one of the promising hybrid quantum-classical algorithms to solve combinatorial optimization problems and it provides great approximate solutions to non-deterministic polynomial-time (NP) hard problems. QAOA maps the given problem into Hilbert space, and then it generates the Hamiltonian for the given objective and constraint. Then, QAOA finds proper parameters from the classical optimization loop in order to optimize the expectation value of the generated Hamiltonian. Based on the parameters, the optimal solution to the given problem can be obtained from the optimum of the expectation value of the Hamiltonian. Inspired by QAOA, a quantum approximate optimization for scheduling (QAOS) algorithm is proposed. The proposed QAOS designs the Hamiltonian of the wireless scheduling problem which is formulated by the maximum weight independent set (MWIS). The designed Hamiltonian is converted into a unitary operator and implemented as a quantum gate operation. After that, the iterative QAOS sequence solves the wireless scheduling problem. The novelty of QAOS is verified with simulation results implemented via Cirq and TensorFlow-Quantum.